QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES.

In this paper, we solve the following quadratic ρ-functional inequalities ..., where ρ is a fixed complex number with |ρ| < 1/8, and ..., where ρ is a fixed complex number with |ρ| < 4. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]